Which pest is characterized by being 1/4 inches chestnut brown and undergoing five molting stages?

The pest characterized by being approximately 1/4 inch in length, chestnut brown in color, and going through five molting stages is indeed the bedbug. These insects undergo a series of nymph stages after hatching from eggs, with each stage requiring a blood meal and a molting process to progress to the next stage. The coloration and the size of bedbugs match the description provided, making them distinct in appearance compared to the other pests listed.

Bedbugs are known for their flat, oval bodies which can easily hide in crevices, and their color can vary from light brown to a deeper reddish-brown after feeding. The specific life cycle stages are crucial for identification, as it highlights their growth process and reliance on blood meals for development. The other pests mentioned, such as the brown-banded cockroaches, American dog ticks, and carpenter ants, have different physical characteristics, life stages, and coloring, which do not align with the description given in the question.